I upgraded my Turtle Beach soundcard over 5 years ago and I notice a big increase in the sound quality. Standard soundcards (and especially onboard soundcards) aren't very good for audio recording. They are better for gaming and stuff like that.
M-Audio makes excellent soundcards at various price ranges, including the Audiophile 2496 ($99) and Delta44 ($150). The Delta44 has 4 inputs and outputs, so you could record 4 tracks at one time. However, it doesn't have built in mic preamps, so if you use a microphone for recording, you'd need to also get a mic preamp (there are lots of cheap options for these as well).
Depending on your needs and price range, there a lot of options that will give far better results than stock soundcards.
-tkr